It is important to develop an efficient right hand thumb technique with the ability to use not only free stroke, but rest stroke as well. A versatile thumb technique is important for dynamic and color flexibility, bringing out bass lines, and muting. The following video discusses the mechanics of the thumb stroke as well as how the stroke can change in different musical situations (ie. single line vs. multi-voice textures/chords). Pay attention to the angle of the thumb to the bass strings, if it is not a large enough angle (roughly 35 degrees) it will be difficult to do a rest stroke with the thumb. If your hand and thumb are positioned correctly, you thumb will slice through the string easily. Your thumb tip joint will be extended while playing a rest stroke and in many instances free stroke as well. The thumb tip joint will flex through the string sometimes while playing chords, multi-part textures, and free stroke, but never for rest stroke. The usage of the tip joint will largely depend on the musical context along with your personal tastes in tone and anatomy of your thumb (ie. length and shape of the thumb).
Practice the basic rest and free strokes with the thumb on the open bass strings while planting i, m, and a on strings 3, 2, and 1 respectively. Planting your fingers on the trebles will ensure you must move from the wrist joint of the thumb and not your entire hand which is a common mistake. Extraneous movement in free stroke thumb is another common error. Allow the straight, efficient movement of the rest stroke thumb train the free stroke thumb to make a straight movement downward toward the index finger. When playing free stroke thumb, it is fine if your thumb touches your index finger during the flexion of the stroke.